On Semantic Update Operators for Answer-Set Programs

Abstract

Logic programs under the stable models semantics, or answer-set programs, provide an expressive rule based knowledge representation framework, featuring formal, declarative and well-understood semantics. However, handling the evolution of rule bases is still a largely open problem. The AGM framework for belief change was shown to give inappropriate results when directly applied to logic programs under a nonmonotonic semantics such as the stable models. Most approaches to address this issue, developed so far, proposed update operators based on syntactic conditions for rule rejection. More recently, AGM revision has been successfully applied to a significantly more expressive semantic characterisation of logic programs based on SE models. This is an important step, as it changes the focus from the evolution of a syntactic representation of a rule base to the evolution of its semantic content. In this paper, we borrow results from the area of belief update to tackle the problem of updating (instead of revising) logic programs. We prove a representation theorem which makes it possible to constructively define any operator satisfying a set of postulates derived from Katsuno and Mendelzon's postulates for belief update. We define a specific operator based on this theorem and compare the behaviour of this operator with syntactic update operators defined in the literature. Perhaps surprisingly, we uncover a very serious drawback in a large class of semantic update operators to which it belongs.